50 MCQ RELATED TO MEASURES OF CENTRAL TENDENCY/ DISPERSION/ AND SKEWNESS
Which of the following is not a measure of central tendency?
A) Mean
B) Median
C) Mode
D) Range
Answer: D) Range
If the average monthly income of an Indian household is calculated, which measure of central tendency is being used?
A) Mean
B) Median
C) Mode
D) Geometric mean
Answer: A) Mean
The median is most appropriate to use when:
A) The data is symmetrically distributed
B) The data has outliers
C) All data points are unique
D) The data has no mode
Answer: B) The data has outliers
Which measure of central tendency is least affected by extreme values in the data set?
A) Mean
B) Median
C) Mode
D) Harmonic mean
Answer: B) Median
In a dataset representing the ages of residents in an Indian village, if the most frequently occurring age is 45, which measure of central tendency does this refer to?
A) Mean
B) Median
C) Mode
D) Range
Answer: C) Mode
Which of the following is not a measure of dispersion?
A) Variance
B) Standard Deviation
C) Interquartile Range
D) Median
Answer: D) Median
The measure of dispersion that is calculated as the average of the squared differences from the mean is:
A) Range
B) Standard Deviation
C) Variance
D) Mean Deviation
Answer: C) Variance
In India, the diversity of incomes in a given state can best be represented by:
A) Mean income
B) Median income
C) Income variance
D) Mode income
Answer: C) Income variance
The range of a dataset is defined as:
A) The difference between the highest and lowest values
B) The average of all values
C) The middle value when data is arranged in ascending order
D) The most frequent value
Answer: A) The difference between the highest and lowest values
A higher value of standard deviation indicates:
A) Less variability in the data
B) More variability in the data
C) No variability in the data
D) Central tendency of the data
Answer: B) More variability in the data
Skewness is a measure of:
A) The central tendency of the data
B) The symmetry of the distribution
C) The variability of the data
D) The correlation of the data
Answer: B) The symmetry of the distribution
A distribution with a longer tail on the right side is said to be:
A) Symmetrical
B) Positively skewed
C) Negatively skewed
D) Normally distributed
Answer: B) Positively skewed
If the mean of a dataset is less than the median, the distribution is:
A) Positively skewed
B) Negatively skewed
C) Symmetrical
D) Bimodal
Answer: B) Negatively skewed
In a perfectly symmetrical distribution, the skewness is:
A) Positive
B) Negative
C) Zero
D) Undefined
Answer: C) Zero
For a given dataset in India, if the distribution of monthly incomes is left-skewed, it implies that:
A) Most people earn below the mean income
B) Most people earn above the mean income
C) The mean income is equal to the median income
D) The mode income is greater than the mean income
Answer: A) Most people earn below the mean income
Which measure of central tendency divides the dataset into two equal parts?
A) Mean
B) Median
C) Mode
D) Quartile
Answer: B) Median
The sum of the deviations of each observation from the mean is:
A) Equal to zero
B) Greater than zero
C) Less than zero
D) Equal to the variance
Answer: A) Equal to zero
In a bimodal distribution, which measure of central tendency is best to describe the data?
A) Mean
B) Median
C) Mode
D) Range
Answer: C) Mode
If the arithmetic mean of a dataset is 50 and there are 10 observations, the sum of all observations is:
A) 50
B) 500
C) 5
D) 100
Answer: B) 500
Which measure of central tendency is calculated by multiplying all the numbers together and then taking the nth root (where n is the number of values)?
A) Arithmetic mean
B) Geometric mean
C) Harmonic mean
D) Median
Answer: B) Geometric mean
The harmonic mean is most appropriate to use when dealing with:
A) Rates and ratios
B) Symmetrical data
C) Nominal data
D) Skewed data
Answer: A) Rates and ratios
In a normal distribution, the mean, median, and mode are:
A) Equal
B) Different
C) Unrelated
D) Based on the range
Answer: A) Equal
Which of the following is not true for a mean?
A) It is sensitive to outliers
B) It uses all data values
C) It can be used for nominal data
D) It is appropriate for interval and ratio data
Answer: C) It can be used for nominal data
When calculating the median of a dataset with an even number of observations, you:
A) Take the middle value
B) Take the average of the two middle values
C) Take the mode
D) Take the mean
Answer: B) Take the average of the two middle values
Which measure of central tendency is most affected by extreme values?
A) Mean
B) Median
C) Mode
D) Interquartile range
Answer: A) Mean
Which measure of dispersion is defined as the difference between the first and third quartiles?
A) Range
B) Variance
C) Standard deviation
D) Interquartile range
Answer: D) Interquartile range
The standard deviation is the square root of the:
A) Mean
B) Variance
C) Range
D) Median
Answer: B) Variance
Which measure of dispersion is expressed in the same units as the original data?
A) Variance
B) Standard deviation
C) Range
D) Mean deviation
Answer: B) Standard deviation
A low value of variance indicates that the data points are:
A) Spread out over a large range
B) Close to the mean
C) Symmetrical
D) Skewed
Answer: B) Close to the mean
The coefficient of variation is calculated by:
A) Dividing the mean by the standard deviation
B) Dividing the standard deviation by the mean
C) Multiplying the mean by the standard deviation
D) Subtracting the mean from the standard deviation
Answer: B) Dividing the standard deviation by the mean
Which of the following measures is not affected by extreme values?
A) Range
B) Variance
C) Interquartile range
D) Standard deviation
Answer: C) Interquartile range
The sum of the squared deviations from the mean divided by the number of observations is the:
A) Standard deviation
B) Mean
C) Median
D) Variance
Answer: D) Variance
When comparing the dispersion of two datasets with different units, the best measure to use is:
A) Range
B) Standard deviation
C) Coefficient of variation
D) Mean deviation
Answer: C) Coefficient of variation
Which measure of dispersion is the simplest to calculate?
A) Range
B) Variance
C) Standard deviation
D) Interquartile range
Answer: A) Range
If all the values in a dataset are the same, the variance is:
A) Zero
B) One
C) Equal to the mean
D) Undefined
Answer: A) Zero
Which of the following is not a measure of skewness?
A) Pearson’s first coefficient
B) Pearson’s second coefficient
C) Spearman’s rho
D) Moment coefficient
Answer: C) Spearman’s rho
A distribution that is skewed to the left has:
A) A long tail on the right
B) A long tail on the left
C) Symmetrical tails
D) No tails
Answer: B) A long tail on the left
In a positively skewed distribution, which of the following is true?
A) Mean < Median < Mode
B) Mean > Median > Mode
C) Mean = Median = Mode
D) Mean < Median > Mode
Answer: B) Mean > Median > Mode
The skewness of a normal distribution is:
A) Positive
B) Negative
C) Zero
D) Undefined
Answer: C) Zero
For a dataset with a skewness coefficient of -2, the distribution is:
A) Symmetrical
B) Positively skewed
C) Negatively skewed
D) Bimodal
Answer: C) Negatively skewed
Which measure is used to describe the shape of the tails in a distribution?
A) Mean
B) Median
C) Kurtosis
D) Range
Answer: C) Kurtosis
The formula for Pearson’s first coefficient of skewness is:
A) (Mean – Mode) / Standard deviation
B) 3(Mean – Median) / Standard deviation
C) (Mean – Median) / Standard deviation
D) (Mean – Mode) / Variance
Answer: A) (Mean – Mode) / Standard deviation
In a dataset, if the skewness coefficient is 1, the distribution is:
A) Symmetrical
B) Moderately positively skewed
C) Moderately negatively skewed
D) Highly skewed
Answer: B) Moderately positively skewed
Which of the following is an example of a measure of central tendency that can be affected by skewness?
A) Median
B) Mode
C) Mean
D) Interquartile range
Answer: C) Mean
A dataset with a skewness coefficient close to zero is:
A) Symmetrical
B) Positively skewed
C) Negatively skewed
D) Bimodal
Answer: A) Symmetrical
The best measure to summarize a dataset with a significant outlier is the:
A) Mean
B) Median
C) Mode
D) Range
Answer: B) Median
Which of the following measures is the least reliable when the dataset contains outliers?
A) Median
B) Mode
C) Mean
D) Interquartile range
Answer: C) Mean
Which measure of dispersion is most sensitive to outliers?
A) Range
B) Interquartile range
C) Variance
D) Standard deviation
Answer: A) Range
For a dataset with a small number of observations, the most stable measure of central tendency is the:
A) Mean
B) Median
C) Mode
D) Geometric mean
Answer: B) Median
The mean deviation is calculated by taking the:
A) Square root of the variance
B) Average of the absolute deviations from the mean
C) Average of the squared deviations from the mean
D) Difference between the maximum and minimum values
Answer: B) Average of the absolute deviations from the mean
